Transition maps at non-resonant hyperbolic singularities are o-minimal

We construct a model complete and o-minimal expansion of the field of real numbers such that, for any planar analytic vector field ξ and any isolated, non-resonant hyperbolic singularity p of ξ, a transition map for ξ at p is definable in . This expansion also defines all convergent generalized power series with natural support and is polynomially bounded.